How to scale object with more vertex to other to fit perfectly?
It should work.. e.g. set your snap as follows, to use the 'Active Element' to snap from, and 'Vertex' to snap to, ensuring the snap is set to affect 'Scale'..

Select all the vertices on the smaller circle, taking care to have a vertex (say one on the X axis?) matching one of the outer circle's vertices active at the end of your selection, and scale it out to snap to its match on the outside.